21.For experimental purposes, a researcher is sent out to measure 5 Douglas-firs in an Interior sample plot which is known to contain 10 Douglas-fir and 15 Hemlock trees. Unfortunately, the researcher has not had a Dendrology course and is not very good at distinguishing between species, so he randomly samples 5 different trees (without replacement).What is the probability that at least 3 of the 5 trees that he measures are really Douglas-firs?

22. The DBH's (Diameters at Breast Height) of the Interior trees in Q 21 (Douglas-firs and Hemlocks taken together) are normally distributed with an average of 20 cm and a standard deviation of 5 cm. What is the probability that the researcher will select a tree that is...

a) less than 15 cm in diameter?

b) between 15 and 20 cm in diameter?

c) greater than 20 cm in diameter?

d) less than 15 cm or greater than 20 cm in diameter?

23.The researcher is working for a forest products company that wishes to buy the biggest 45% of the Douglas-firs and Hemlocks from an Interior cut block. Based on the information in Q 22, what is the minimum diameter that the company should set its debarkers at?[*Exercise 6.12]

24.The forest products company (in Q 23) uses its excess chips and sawdust as furnish for the manufacture of particleboard. The particleboard plant has a variable forming machine that discharges furnish in amounts that are normally distributed with a mean,kg, and a standard deviation of 2.57 kg.If the company wishes to use the forming machine to fill a forming belt that holds (a maximum of) 200 kg of furnish at once and only wants to overfill the forming belt 1% of the time, at what value ofshould the company set its forming machine?

25.A chip used in the production of particleboard (Q 24) has a 15% chance of containing excessive bark. What is the probability of having more than 860 bark-free chips in a batch of 1,000?

26.It is known that the service lives of the forming belts (in Q24) are normally distributed with a mean of 12 years and a standard deviation of 2 years. If the manufacturer of these forming belts is willing to replace free of charge any belt that fails while under warranty, how long a warranty should they offer if they are only willing to replace 3% of the belts that fail?